Finite Group Databasebeta

← C2×#13079631 #15625034

Subgroups — C2×#13079631 #15625034

Order 2816.

2834 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66927C211yesmaximal, characteristic, complemented
2#13079631C2116yesmaximal, direct product factor
3C2×#10622671C212yesmaximal, complemented
4C2×#10622680C212yesmaximal, complemented
5C2×#10622640C212yesmaximal, complemented
6C2×#10622628C212yesmaximal, complemented
7C2×#10622659C212yesmaximal, complemented
8C2×#10622649C212yesmaximal, complemented
9C2×#10622539C211yesmaximal, characteristic, complemented
10C2×C11×#529C211yesmaximal, characteristic, complemented
11C23×D44—21no—
12C23×D44—21no—
13C23×D44C2212yes—
14C11×#529—24no—
15C11×#529C2218yescomplemented
16C2×C11×#126—21no—
17C2×C11×#125C2211yescharacteristic, complemented
18C2×C11×#124C2211yescharacteristic, complemented
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic, complemented
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic, complemented
25C2×C11×#117—21no—
26C22×C42×C11C2211yescharacteristic
27C22×#4325C2214yescomplemented
28C22×#4323C2214yescomplemented
29C2×#66927—24no—
30C2×#66927—21no—
31C2×#66927—21no—
32C2×#66927C2212yes—
33C2×#66927C2212yes—
34C2×#66927C2218yescomplemented
35C2×C22⋊(C11⋊C8)C2212yes—
36#10622680C22116yescomplemented
37#10622671C22116yescomplemented
38#10622659C22116yescomplemented
39#10622649C22116yescomplemented
40#10622640C22116yescomplemented
41#10622628C22116yescomplemented
42C2×#66873C2214yescomplemented
43C2×#66873C2214yescomplemented
44#10622539C2218yescomplemented
45C2×C4⋊(C11⋊C8)C2212yescomplemented
46C2×#66867C2212yescomplemented
47C24×D11—22no—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×D44—22no—
56C22×D44—24no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—22no—
60C22×D44—22no—
61C22×D44—28no—
62C22×D44—28no—
63C22×D44—48no—
64C22×D44—48no—
65C22×D44—48no—
66C22×D44C2314yes—
67C22×D44C2318yes—
68C11×#126—28no—
69C11×#125—22no—
70C11×#125C2314yescomplemented
71C11×#124—22no—
72C11×#124C2314yescomplemented
73C11×#123—28no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8C2314yes—
76C11×#121—22no—
77C11×#121C2314yes—
78C4×Q8×C11—22no—
79C4×Q8×C11C2314yescomplemented
80C4×D4×C11—28no—
81C4×D4×C11—22no—
82C4×D4×C11C2314yescomplemented
83C11×#117—28no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C42×C11—21no—
96C2×C42×C11D411yescharacteristic
97C2×C42×C11D411yescharacteristic
98C2×C42×C11D414yes—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2314yes—
102C2×#4325—48no—
103C2×#4325C23116yescomplemented
104C2×#4323—48no—
105C2×#4323C23116yescomplemented
106C22×C11⋊C8C2314yes—
107#66927—24no—
108#66927—24no—
109#66927—28no—
110#66927—28no—
111#66927C2318yes—
112#66927C2318yes—
113C22⋊(C11⋊C8)C2318yes—
114#66873C23116yescomplemented
115#66873C23116yescomplemented
116C4⋊(C11⋊C8)C2318yescomplemented
117#66867C2318yescomplemented
118C2×#3217—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11C2×D411yescharacteristic
121C23×D11—28no—
122C23×D11—24no—
123C23×D11—48no—
124C23×D11—48no—
125C23×D11—48no—
126C2×Q8×C11—21no—
127C2×Q8×C11—24no—
128C2×Q8×C11C2412yes—
129C2×D4×C11—24no—
130C2×D4×C11—21no—
131C2×D4×C11—24no—
132C2×D4×C11—44no—
133C2×D4×C11C2412yes—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—44no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2412yes—
151C22×C4×C11C2411yescharacteristic
152C2×D44—28no—
153C2×D44—24no—
154C2×D44—28no—
155C2×D44—28no—
156C2×D44—28no—
157C2×D44—28no—
158C2×D44—28no—
159C2×D44—28no—
160C2×D44—416no—
161C2×D44—48no—
162C2×D44—48no—
163C2×D44—48no—
164C2×D44—48no—
165C2×D44—432no—
166C2×D44—416no—
167C2×D44—432no—
168C2×D44—48no—
169C2×D44C2418yes—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C2412yes—
177C11×C4⋊C4C2412yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C42×C11—24no—
184C42×C11C2×D414yes—
185C42×C11C2×D412yes—
186C42×C11C2×D412yes—
187C42×C11C2×D414yes—
188C42×C11C2412yes—
189C42×C11C2412yes—
190#4325—416no—
191#4323—416no—
192C2×C11⋊C8—28no—
193C2×C11⋊C8C2418yes—
194C22×#127—111no—
195C2×#529D1111yescharacteristic, complemented
196#3217—1116no—
197C2×#496—112no—
198C2×#490—112no—
199C2×#460—112no—
200C2×#459—112no—
201C2×#450—112no—
202C2×#447—112no—
203C2×#432—111no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11AGL(1,ℤ/8)14yes—
211C23×C11C22×D412yes—
212C23×C11C22×D411yescharacteristic
213C22×D11—28no—
214C22×D11—416no—
215C22×D11—416no—
216C22×D11—48no—
217C22×D11—416no—
218C22×D11—48no—
219C22×D11—48no—
220C22×D11—832no—
221Q8×C11—24no—
222Q8×C11—42no—
223D4×C11—24no—
224D4×C11—48no—
225D4×C11—42no—
226C2×C4×C11—22no—
227C2×C4×C11—28no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—28no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—48no—
241C2×C4×C11AGL(1,ℤ/8)14yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D412yes—
248C2×C4×C11H(5,𝔽2)14yes—
249C2×C4×C11C2511yescharacteristic
250D44—28no—
251D44—28no—
252D44—416no—
253D44—416no—
254D44—416no—
255D44—416no—
256D44—48no—
257D44—416no—
258C11⋊C8—28no—
259C23×D4—112no—
260C23×D4—221no—
261C23×D4—221no—
262C22×SD16—114no—
263C22×D8—114no—
264C2×#127—112no—
265C2×#127—112no—
266C2×#127—118no—
267C2×#127—221no—
268C2×#127—221no—
269C2×#127—224no—
270#529—24no—
271#529C2×D1118yescomplemented
272C2×#126—21no—
273C2×#125C2×D1111yescharacteristic, complemented
274C2×#124C2×D1111yescharacteristic, complemented
275C2×#123—21no—
276C2×C22⋊Q8C2×D1111yescharacteristic
277C2×#121C2×D1111yescharacteristic
278C2×C4×Q8C2×D1111yescharacteristic, complemented
279C2×C4×D4—21no—
280C2×C4×D4C2×D1111yescharacteristic, complemented
281C2×#117—21no—
282C22×C42C2×D1111yescharacteristic
283#496—1116no—
284#490—1116no—
285#460—1116no—
286#459—1116no—
287#450—1116no—
288#447—1116no—
289#432—118no—
290C2×C4⋊C8—112no—
291C2×#102—114no—
292C2×#102—114no—
293C2×C22⋊C8—112no—
294C2×#97—112no—
295C22×C11—22no—
296C22×C11—28no—
297C22×C11—22no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—84no—
302C22×C11#53512yes—
303C22×C11C2×AGL(1,ℤ/8)14yes—
304C22×C11C2×AGL(1,ℤ/8)12yes—
305C22×C11C2×AGL(1,ℤ/8)12yes—
306C22×C11C23×D411yescharacteristic
307C2×D11—48no—
308C2×D11—48no—
309C2×D11—48no—
310C2×D11—832no—
311C2×D11—816no—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—22no—
315C4×C11—22no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11#53512yes—
320C4×C11C2×AGL(1,ℤ/8)14yes—
321C4×C11C2×H(5,𝔽2)12yes—
322C25—222no—
323C22×Q8C22×D1111yescharacteristic
324C22×D4—21no—
325C22×D4—114no—
326C22×D4—118no—
327C22×D4—228no—
328C22×D4—228no—
329C22×D4—222no—
330C22×D4—222no—
331C22×D4—222no—
332C22×D4—222no—
333C22×D4—224no—
334C22×D4—222no—
335C22×D4—448no—
336C22×D4—448no—
337C22×D4—448no—
338C22×D4C22×D1111yescharacteristic
339C23×C4—21no—
340C23×C4C22⋊D1111yescharacteristic
341C23×C4C22⋊D1111yescharacteristic
342C23×C4C22×D1111yescharacteristic
343C2×SD16—1116no—
344C2×SD16—448no—
345C2×D8—1116no—
346C2×D8—448no—
347C22×C8—114no—
348#127—118no—
349#127—118no—
350#127—228no—
351#127—224no—
352#127—224no—
353#127—228no—
354#126—28no—
355#125—22no—
356#125C22×D1114yescomplemented
357#124—22no—
358#124C22×D1114yescomplemented
359#123—28no—
360C22⋊Q8—22no—
361C22⋊Q8C22×D1114yes—
362#121—22no—
363#121C22×D1114yes—
364C4×Q8—22no—
365C4×Q8C22×D1114yescomplemented
366C4×D4—28no—
367C4×D4—22no—
368C4×D4C22×D1114yescomplemented
369#117—28no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—21no—
382C2×C42C22⋊D1111yescharacteristic
383C2×C42C22⋊D1111yescharacteristic
384C2×C42C22⋊D1114yes—
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1114yes—
388C4⋊C8—118no—
389#102—1116no—
390#102—1116no—
391C22⋊C8—118no—
392#97—118no—
393C2×C11—24no—
394C2×C11—82no—
395C2×C11#321714yescomplemented
396C2×C11C2×#53511yescharacteristic
397C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
398C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
399D11—88no—
400C24—21no—
401C24—228no—
402C24—224no—
403C24—448no—
404C24—448no—
405C24—448no—
406C24C2×C22⋊D1111yescharacteristic
407C2×Q8—21no—
408C2×Q8—24no—
409C2×Q8C23×D1112yes—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—21no—
413C2×D4—44no—
414C2×D4—118no—
415C2×D4—228no—
416C2×D4—228no—
417C2×D4—228no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—228no—
421C2×D4—228no—
422C2×D4—224no—
423C2×D4—4416no—
424C2×D4—4432no—
425C2×D4—448no—
426C2×D4—448no—
427C2×D4—448no—
428C2×D4—448no—
429C2×D4—4432no—
430C2×D4—4416no—
431C2×D4—448no—
432C2×D4C23×D1112yes—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—44no—
441C22×C4C2×C22⋊D1114yes—
442C22×C4C2×C22⋊D1114yes—
443C22×C4C2×C22⋊D1112yes—
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C23×D1112yes—
450C22×C4C23×D1111yescharacteristic
451SD16—4416no—
452D8—4416no—
453C2×C8—118no—
454C2×C8—228no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4C23×D1112yes—
462C4⋊C4C23×D1112yes—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C42—24no—
469C42C2×C22⋊D1114yes—
470C42C2×C22⋊D1112yes—
471C42C2×C22⋊D1112yes—
472C42C2×C22⋊D1114yes—
473C42C23×D1112yes—
474C42C23×D1112yes—
475C11C2×#321711yescharacteristic, complemented, Sylow
476C23—22no—
477C23—22no—
478C23—22no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—228no—
483C23—4416no—
484C23—4416no—
485C23—4416no—
486C23—448no—
487C23—448no—
488C23—448no—
489C23—8832no—
490C23#6700214yes—
491C23C22×C22⋊D1112yes—
492C23C22×C22⋊D1111yescharacteristic
493Q8—24no—
494Q8—42no—
495D4—24no—
496D4—48no—
497D4—42no—
498D4—228no—
499D4—228no—
500D4—4416no—
501D4—4416no—
502D4—4416no—
503D4—4416no—
504D4—4416no—
505D4—448no—
506C2×C4—28no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—28no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—48no—
521C2×C4#6700214yes—
522C2×C4#6704214yes—
523C2×C4C22×C22⋊D1112yes—
524C2×C4C22×C22⋊D1112yes—
525C2×C4C22×C22⋊D1112yes—
526C2×C4C22×C22⋊D1112yes—
527C2×C4C22×C22⋊D1112yes—
528C2×C4C22×C22⋊D1111yescharacteristic
529C2×C4C24×D1111yescharacteristic
530C8—228no—
531C22—22no—
532C22—28no—
533C22—22no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—84no—
538C22—448no—
539C22—448no—
540C22—448no—
541C22—8832no—
542C22—8816no—
543C22C2×#6700214yes—
544C22C2×#6700212yes—
545C22C2×#6700212yes—
546C22#1062336112yes—
547C22C23×C22⋊D1111yescharacteristic
548C4—22no—
549C4—22no—
550C4—22no—
551C4—22no—
552C4—42no—
553C4—42no—
554C4—42no—
555C4C2×#6700214yes—
556C4#1062336112yes—
557C4C2×#6704212yes—
558C2—24no—
559C2—82no—
560C2—888no—
561C2#1307963114yesdirect product factor
562C2C2×#1062336111yescharacteristic
563C2C22×#6700211yescharacteristic
564C2C22×#6700211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
hypercenterC2×#529D11
hypocenterC11C2×#3217
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#66927C2semidirect
2. #13079631C2direct (N × H)
3. C2×#10622671C2semidirect
4. C2×#10622680C2semidirect
5. C2×#10622640C2semidirect
6. C2×#10622628C2semidirect
7. C2×#10622659C2semidirect
8. C2×#10622649C2semidirect
9. C2×#10622539C2semidirect
10. C2×C11×#529C2semidirect
15. C11×#529C22semidirect
17. C2×C11×#125C22semidirect
18. C2×C11×#124C22semidirect
22. C2×C4×Q8×C11C22semidirect
24. C2×C4×D4×C11C22semidirect
27. C22×#4325C22semidirect
28. C22×#4323C22semidirect
34. C2×#66927C22semidirect
36. #10622680C22semidirect
37. #10622671C22semidirect
38. #10622659C22semidirect
39. #10622649C22semidirect
40. #10622640C22semidirect
41. #10622628C22semidirect
42. C2×#66873C22semidirect
43. C2×#66873C22semidirect
44. #10622539C22semidirect
45. C2×C4⋊(C11⋊C8)C22semidirect
46. C2×#66867C22semidirect
70. C11×#125C23semidirect
72. C11×#124C23semidirect
79. C4×Q8×C11C23semidirect
82. C4×D4×C11C23semidirect
103. C2×#4325C23semidirect
105. C2×#4323C23semidirect
114. #66873C23semidirect
115. #66873C23semidirect
116. C4⋊(C11⋊C8)C23semidirect
117. #66867C23semidirect
195. C2×#529D11semidirect
271. #529C2×D11semidirect
273. C2×#125C2×D11semidirect
274. C2×#124C2×D11semidirect
278. C2×C4×Q8C2×D11semidirect
280. C2×C4×D4C2×D11semidirect
356. #125C22×D11semidirect
358. #124C22×D11semidirect
365. C4×Q8C22×D11semidirect
368. C4×D4C22×D11semidirect
395. C2×C11#3217semidirect
475. C11C2×#3217semidirect
561. C2#13079631direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669272
#130796312
C2×#106226712
C2×#106226802
C2×#106226402
C2×#106226282
C2×#106226592
C2×#106226492
C2×#106225392
C2×C11×#5292
C2×#321711